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AT&T has wagered $6-billion (U.S.) that it can beat regulatory opposition and buy T-Mobile USA. The net benefit of the $39-billion purchase could be in the same ballpark. But few experts thought the odds of getting the deal approved were better than 50-50. With the U.S. Justice Department now opposing the deal, it looks as if Randall Stephenson, the AT&T chief executive officer, and his board made a bad call.

Just do the math. The financial cost of failure is the break fee, which comprises $3-billion in cash and similar value in spectrum and other goodies that AT&T will hand over to Deutsche Telekom, T-Mobile's owner, if regulators nix the deal.

On the benefit side, it's a good strategic fit and AT&T has said synergies in a broad sense could be worth more than the entire purchase price. Based on past deals, that sounds optimistic. But suppose the merger does at least deliver $3-billion in annual savings after three years, as AT&T promises. The present value of these, after tax and $7-billion of up-front costs, is perhaps $11-billion. To be extra generous, assume the firm can scale that up and extract $15-billion of value.

That benefit needs to be reduced by the premium AT&T has offered for T-Mobile. The deal value, at 7.1 times estimated EBITDA for 2011, is about a third richer than the valuation attached to the other three big U.S. telecom carriers – meaning the premium is about $9-billion. Net that off, and AT&T would benefit to the tune of $6-billion or so if the deal goes ahead – the same as the cost if it doesn't.

Before the deal was announced, most people thought such a merger had no chance. After it was unveiled, most on Wall Street thought it was a toss-up at best whether regulators would let it happen. There's no sign that AT&T's top-notch lawyers differed wildly in their assessment.

So assuming the odds of approval were roughly even, Mr. Stephenson and his board chose to sink management time, preparatory costs and the company's credibility into an effort with a mathematically expected return of around zero. That's a poor use of resources. The bet could still come good, but now that regulators have opposed the deal, the more probable outcome is that AT&T has to shell out the break fee. If the merger falls apart, the buck stops in the company's boardroom.



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